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MCRN

Complex Energy Systems

This is the opening guest lecture for the Electric Grid Focus Group. Dr. Michael Chertkov of Los Alamos National Lab describes the statistical and mathematical problems arising in complex energy systems, including the electric grid and gas networks. Systems with high penetration of renewable energy …
  • Resource Presentations
MCRN

Geometric Dynamical Systems: Manifolds and Stability Part III

This is the final part of a series of dynamical systems lectures on the center, stable and unstable manifold theorems. This short lecture series was part of the MCRN Mathematics of Climate Modelling Course taught at the University of North Carolina by Chris Jones in 2013. This course was a second ye…
  • Resource Presentations
MCRN

Realistic modeling and analysis of synchronization dynamics in power-grid networks

An imperative condition for the functioning of a power-grid network is that its power generators remain synchronized. Disturbances can prompt desynchronization, which is a process that has been involved in large power outages. In this talk I will first give a comparative review of three leading mode…
  • Resource Presentations
MCRN

Computational Techniques for Lyapunov Exponents and Vectors

In this talk we present computational techniques for Lyapunov exponents and vectors based upon continuous matrix factorizations (QR and SVD). We outline the techniques, their well-posedness, error analysis/perturbation theory, and describe codes we have developed. We then discuss application of thes…
  • Resource Presentations
MCRN

Synchronization in power grid networks

This survey discusses Master Stability Function (MSF) analysis for determining stability of synchronization of coupled oscillators on network. In addition, we briefly discuss the derivation of the Swing equation that determine the dynamics of a node in power grid network, and different models of the…
  • Resource Presentations
MCRN

Geometric Dynamical Systems: Manifolds and Stability Part I

This is the first part of a series of dynamical systems lectures on the center, stable and unstable manifold theorems. This short lecture series was part of the MCRN Mathematics of Climate Modelling Course taught at the University of North Carolina by Chris Jones in 2013. This course was a second ye…
  • Resource Presentations
MCRN

Geometric Dynamical Systems: Manifolds and Stability Part II

This is the first part of a series of dynamical systems lectures on the center, stable and unstable manifold theorems. This short lecture series was part of the MCRN Mathematics of Climate Modelling Course taught at the University of North Carolina by Chris Jones in 2013. This course was a second ye…
  • Resource Presentations

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